OS X Lion came installed on Mac Air, can I also install to Mac Mini for free?

I bought a new Mac Air that comes preinstalled with OS X Lion. I know if you purchase OS X Lion from the App Store, you are able to install the software on both a desktop and laptop. Can I install OS X Lion for free on my Mac Mini since I technically just purchased OS X Lion (when I bought my new Mac Air)?

Thanks,
Zack